Image Inpainting Based on Total Variation Algorithm

This document presents a MATLAB implementation of image inpainting based on the Total Variation (TV) algorithm. The TV regularization method is a widely used approach for image restoration that effectively recovers damaged images. Through mathematical modeling and optimization of images, this algorithm can repair defects and damaged regions in images. The implementation utilizes MATLAB's optimization toolbox and matrix operations to solve the variational problem, typically involving gradient descent or primal-dual methods for minimizing the TV functional. In this document, I will explain the algorithm's principles and implementation steps in detail, covering key aspects such as the regularization parameter selection, edge-preserving properties, and numerical solution techniques. The provided MATLAB code demonstrates how to set up the energy functional, implement the optimization solver, and handle boundary conditions. The code includes functions for calculating gradients, divergence operators, and implementing iterative schemes for convergence. This documentation aims to help readers better understand and apply TV-based image inpainting methods in practical scenarios, with particular attention to numerical stability and computational efficiency considerations.